Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption. This is a joint work with Xiao-Guang Lv and Fang Li.

This presentation is part of Minisymposium “MS49 - Image Restoration, Enhancement and Related Algorithms (4 parts)”
organized by: Weihong Guo (Case Western Reserve University) , Ke Chen (University of Liverpool) , Xue-Cheng Tai (Hong Kong Baptist University) , Guohui Song (Clarkson University) .

Authors:

Tieyong Zeng (Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T.)

Keywords:

blind image deconvolution, image deblurring, image enhancement, image reconstruction, inverse problems, nonlinear optimization, primal-dual, regularization, star norm, total variation